We analytically derive an expression for the optical field describing the spin Hall effect of a paraxial Gaussian beam in a lenslike inhomogeneous medium using the matrix optics method. Interestingly, we found changes in the phase structure and rotation of the polarization of the Gaussian beam induced by spin-orbit coupling, in addition to a polarization-dependent transverse deflection of the entire beam. This rotation of the polarization of the beam is not the result of the Berry phase. In addition, we show that the intrinsic optical angular momentum density of the beam is changed due to the spin-orbit coupling, and we also know that polarization-dependent rotation of the beam occurs when a circularly polarized nonaxisymmetric beam propagates in a lenslike inhomogeneous medium. Our results provide further potential applications of the spin Hall effect of light in optical signal processing.